Analysis of the properties influencing film rating over 7

student number: 3026884, 2995341, 2897872, 2971937

1 Introduction

The goal of this analysis is to determine which film properties influence whether a movie is rated above 7 on IMDB. We will use a Generalized Linear Model (GLM) along with other machine learning models for comparison.

2 Data Loading and Cleaning

film <- read.csv("dataset07.csv")

# Check structure and missing values
str(film)
'data.frame':   2387 obs. of  7 variables:
 $ film_id: int  39891 33810 20282 33131 50633 37020 55337 28037 13291 11359 ...
 $ year   : int  2003 2004 1941 1959 1917 1934 2003 1988 1981 1935 ...
 $ length : int  75 120 78 106 70 64 91 101 78 7 ...
 $ budget : num  10.9 19.6 11.7 12 14.8 11.6 12.6 10.1 14.2 6.6 ...
 $ votes  : int  17 21 14 14 9 8 182 274 61 10 ...
 $ genre  : chr  "Action" "Documentary" "Action" "Drama" ...
 $ rating : num  4.4 7.3 2.7 4.9 5.6 4.7 4.4 4.3 4.3 8.8 ...
skim(film)
Data summary
Name film
Number of rows 2387
Number of columns 7
_______________________
Column type frequency:
character 1
numeric 6
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
genre 0 1 5 11 0 7 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
film_id 0 1.00 29941.55 16971.73 33.0 14799.0 30259.0 44669.5 58780.0 ▇▇▇▇▇
year 0 1.00 1976.87 23.74 1894.0 1958.0 1984.0 1998.0 2005.0 ▁▁▃▃▇
length 92 0.96 81.41 37.67 1.0 72.0 90.0 100.0 399.0 ▃▇▁▁▁
budget 0 1.00 11.95 2.97 2.1 10.0 12.0 13.9 23.7 ▁▅▇▂▁
votes 0 1.00 658.97 4370.04 5.0 12.0 32.0 118.0 103854.0 ▇▁▁▁▁
rating 0 1.00 5.41 2.07 0.7 3.7 4.7 7.8 9.2 ▁▇▆▂▇
# Remove missing values
film <- film %>% drop_na()

# Convert categorical variables
film$genre <- as.factor(film$genre)

3 Exploratory Data Analysis

summary(film)
    film_id           year          length           budget     
 Min.   :   33   Min.   :1894   Min.   :  1.00   Min.   : 2.10  
 1st Qu.:14950   1st Qu.:1958   1st Qu.: 72.00   1st Qu.:10.00  
 Median :30294   Median :1984   Median : 90.00   Median :12.00  
 Mean   :30045   Mean   :1977   Mean   : 81.41   Mean   :11.95  
 3rd Qu.:44922   3rd Qu.:1998   3rd Qu.:100.00   3rd Qu.:14.00  
 Max.   :58780   Max.   :2005   Max.   :399.00   Max.   :23.70  
                                                                
     votes                genre         rating     
 Min.   :     5   Action     :680   Min.   :0.700  
 1st Qu.:    12   Animation  :160   1st Qu.:3.700  
 Median :    32   Comedy     :549   Median :4.700  
 Mean   :   668   Documentary:132   Mean   :5.416  
 3rd Qu.:   120   Drama      :654   3rd Qu.:7.800  
 Max.   :103854   Romance    : 15   Max.   :9.200  
                  Short      :105                  
#Histograms of IMDB ratings 
ggplot(film, aes(x = rating)) +
  geom_histogram(binwidth = 0.5, fill = "steelblue", color = "black") +
  labs(x = "IMDB Rating", y = "Frequency", title = "Distribution of IMDB Ratings")

#Barplot of Film Counts by Genre
ggplot(film, aes(x = factor(genre))) +
  geom_bar(fill = "skyblue", color = "black") +
  labs(x = "Genre", y = "Count of Films", title = "Count of Films by Genre")

#Scatterplot of Budget vs Rating
ggplot(film, aes(x = budget, y = rating)) +
  geom_point(color = "steelblue") +
  labs(x = "Budget (Millions)", y = "IMDB Rating", title = "Rating vs Budget")+
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)

#Scatterplot of Votes vs Rating
VR1 <-ggplot(film, aes(x = votes, y = rating)) +
  geom_point(alpha = 0.5) +
  labs(title = "Votes vs IMDB Rating", x = "Number of Votes", y = "IMDB Rating")+
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)

#Scatterplot  of Log(Votes) vs Rating
VR2 <- ggplot(film, aes(x = log(votes), y = rating)) +
  geom_point(alpha = 0.5) +
  labs(title = "Log(Votes) vs IMDB Rating", x = "Log(Votes)", y = "IMDB Rating")+
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)

VR <- subplot(VR1, VR2)
VR
#Scatterplot of Film Length vs Rating
LR1 <- ggplot(film, aes(x = length, y = rating)) +
  geom_point(alpha = 0.5) +
  labs(title = " Film Length vs IMDB Rating", x = " Film Length (Minutes)", y = "IMDB Rating")+
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)

#Scatterplot of log(Film Length) vs Rating
LR2 <- ggplot(film, aes(x = log(length), y = rating)) +
  geom_point(alpha = 0.5) +
  labs(title = " log(Film Length) vs IMDB Rating", x = " Log(Film Length)", y = "IMDB Rating")+
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)

LR <- subplot(LR1, LR2)
LR
#Boxplot of Year vs Rating by duration
film$year_group <- cut(film$year, 
                             breaks = c(1894, 1904, 1914, 1924, 1934, 1944, 1954, 1964, 1974, 1984, 1994,2006), 
                             labels = c(1:11),right=FALSE)  
ggplot(film, aes(x = year_group, y = rating, fill = year_group)) +
  geom_boxplot(na.rm = TRUE) +
  labs(title = "IMDB Rating by Year Group", x = "Year Group", y = "IMDB Rating") +
  geom_hline(yintercept = 7, linetype = "dashed", color = "red", size = 1)+
  scale_fill_discrete(name = "Year Group", 
                      labels = c("1894-1904", 
                                 "1904-1914", 
                                 "1914-1924", 
                                 "1924-1934", 
                                 "1934-1944", 
                                 "1944-1954", 
                                 "1954-1964", 
                                 "1964-1974", 
                                 "1974-1984", 
                                 "1984-1994", 
                                 "1994-2005")) 

4 Creating the Binary Outcome Variable

film$rating_binary <- ifelse(film$rating > 7, 1, 0)

5 Correlation Analysis

library(GGally)
library(dplyr)

# Select only numeric variables, excluding 'film_id' and 'rating'
film_numeric <- film %>%
  dplyr::select(where(is.numeric)) %>%
  dplyr::select(-film_id, -rating)  # Remove 'film_id' and 'rating'

# Create the correlation plot
ggpairs(film_numeric, cardinality_threshold = NULL, title = "Correlation Plot of Numeric Features")

library(corrplot)
# Compute correlation matrix without 'film_id' and 'rating'
cor_matrix <- cor(film_numeric , use = "complete.obs")

# Plot the correlation matrix as a heatmap
corrplot(cor_matrix, 
         method = "color",      # Use color shading
         type = "upper",        # Show only upper triangle
         tl.cex = 0.8,          # Adjust text size
         tl.col = "black",      # Label color
         addCoef.col = "black", # Add correlation values in black
         number.cex = 0.8)      # Adjust correlation value size

6 Variable Selection

# Univariate Logistic Regression
variables <- c("year", "length", "budget", "votes")
univariate_results <- sapply(variables, function(var) {
  model <- glm(rating_binary ~ get(var), data = film, family = binomial)
  summary(model)$coefficients[2,4]
})
univariate_results
        year       length       budget        votes 
6.776190e-01 1.842618e-92 1.768745e-31 2.350198e-01 

7 Stepwise Regression

full_model <- glm(rating_binary ~ year + length + budget + votes + genre, data = film, family = binomial)
stepwise_model <- stepAIC(full_model, direction = "both")
Start:  AIC=1311.03
rating_binary ~ year + length + budget + votes + genre

         Df Deviance    AIC
- year    1   1290.1 1310.1
<none>        1289.0 1311.0
- votes   1   1293.0 1313.0
- length  1   1599.9 1619.9
- budget  1   1663.1 1683.1
- genre   6   2110.1 2120.1

Step:  AIC=1310.07
rating_binary ~ length + budget + votes + genre

         Df Deviance    AIC
<none>        1290.1 1310.1
+ year    1   1289.0 1311.0
- votes   1   1294.3 1312.3
- length  1   1609.3 1627.3
- budget  1   1664.8 1682.8
- genre   6   2130.3 2138.3
summary(stepwise_model)

Call:
glm(formula = rating_binary ~ length + budget + votes + genre, 
    family = binomial, data = film)

Coefficients:
                   Estimate Std. Error z value Pr(>|z|)    
(Intercept)      -3.618e+00  4.428e-01  -8.170 3.09e-16 ***
length           -5.129e-02  3.566e-03 -14.382  < 2e-16 ***
budget            4.962e-01  3.147e-02  15.770  < 2e-16 ***
votes             3.609e-05  1.672e-05   2.159   0.0309 *  
genreAnimation   -1.974e-01  3.378e-01  -0.584   0.5590    
genreComedy       2.749e+00  1.835e-01  14.983  < 2e-16 ***
genreDocumentary  4.840e+00  4.098e-01  11.809  < 2e-16 ***
genreDrama       -2.040e+00  2.580e-01  -7.907 2.64e-15 ***
genreRomance     -1.361e+01  3.138e+02  -0.043   0.9654    
genreShort        4.209e+00  1.050e+00   4.008 6.12e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 2982.5  on 2294  degrees of freedom
Residual deviance: 1290.1  on 2285  degrees of freedom
AIC: 1310.1

Number of Fisher Scoring iterations: 14

8 Multicollinearity Check (VIF)

vif_values1 <- vif(full_model)
vif_values1
           GVIF Df GVIF^(1/(2*Df))
year   1.097052  1        1.047403
length 2.684298  1        1.638383
budget 1.536962  1        1.239743
votes  1.042504  1        1.021031
genre  3.084105  6        1.098401
vif_values2 <- vif(stepwise_model)
vif_values2
           GVIF Df GVIF^(1/(2*Df))
length 2.544746  1        1.595226
budget 1.537080  1        1.239790
votes  1.039750  1        1.019681
genre  3.020513  6        1.096495

9 Principal Component Analysis (no need)

10 Model Comparison

# Logistic Regression
logit_model <- glm(rating_binary ~ year + budget + votes, data = film, family = binomial)
summary(logit_model)

Call:
glm(formula = rating_binary ~ year + budget + votes, family = binomial, 
    data = film)

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -8.042e-01  3.758e+00  -0.214    0.831    
year        -1.065e-03  1.901e-03  -0.560    0.575    
budget       1.901e-01  1.628e-02  11.678   <2e-16 ***
votes       -1.417e-05  1.231e-05  -1.151    0.250    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 2982.5  on 2294  degrees of freedom
Residual deviance: 2830.3  on 2291  degrees of freedom
AIC: 2838.3

Number of Fisher Scoring iterations: 4
# Random Forest
rf_model <- randomForest(rating_binary ~ year + budget + votes, data = film, ntree = 500, importance = TRUE)
print(rf_model)

Call:
 randomForest(formula = rating_binary ~ year + budget + votes,      data = film, ntree = 500, importance = TRUE) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 1

          Mean of squared residuals: 0.208054
                    % Var explained: 9
varImpPlot(rf_model)

# Lasso Regression
x <- model.matrix(rating_binary ~ year + budget + votes, data = film)[,-1]
y <- film$rating_binary
lasso_model <- cv.glmnet(x, y, alpha = 1, family = "binomial")
coef(lasso_model, s = "lambda.min")
4 x 1 sparse Matrix of class "dgCMatrix"
                       s1
(Intercept) -2.679275e+00
year         .           
budget       1.709116e-01
votes       -1.616137e-06

11 Model Evaluation and Prediction

# Model Performance Metrics
logit_pred <- predict(logit_model, type = "response")
logit_class <- ifelse(logit_pred > 0.5, 1, 0)
table(logit_class, film$rating_binary)
           
logit_class    0    1
          0 1375  635
          1  108  177
# Random Forest Prediction
rf_pred <- predict(rf_model, type = "class")
table(rf_pred, film$rating_binary)
                      
rf_pred                0 1
  0                    1 0
  0.000304785126485629 1 0
  0.00124999999999981  1 0
  0.0013157894736836   1 0
  0.00142045454545364  1 0
  0.00212765957446753  1 0
  0.0030068728522335   1 0
  0.00394088669950737  1 0
  0.00395480225988626  1 0
  0.00531951640759892  1 0
  0.00689655172413717  1 0
  0.00726744186046441  1 0
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12 Conclusion

Based on the analysis, we found that budget and votes are significant predictors of IMDB ratings. The logistic regression and random forest models provided strong predictive capabilities, while PCA did not significantly improve the model. Further improvements could be made using ensemble methods or additional feature engineering.